i was right!

this grand design book really is a curious and thought-provoking book. i remember one of my high school teacher's saying, just before the end of class one day, that the shortest distance between two points isn't always a straight line. i was floored. how can this be?

i was so taken by his statement that it's the only thing i remembered from ANY of my math classes from 9th grade on. i didn't care for math, having lost lots of ground when i moved in 7th grade and ended up with this HORRIBLE teacher who knew absolutely nothing about math and couldn't answer any of my questions. i was in tears because i knew it was the end of math and me.

but back to the straight line -- i always remembered his comment and one day back in about 1989 when we were hiking in the cascades, i finally realized i knew what his comment meant. we were following a trail along a mountainside (straight up on the left, straight down on the right) and i could see the trail we would be reaching shortly, across the valley on the right. our path was going to curve back around almost 180 degrees.

well, it was obvious! it was much shorter to continue on our drastically curving trail than to cut off to the right, in a straight line which just happened to go down and back up. it was so cool to KNOW that.

and here it is on page 101 of hawking's book -- "The geometry of curved spaces such as the earth's surface is not the Euclidean geometry we are familiar with." it goes on to show an intriguing diagram and then explains that if you took a route from new york to madrid on a flat map, it would be a straight line of 3,707 miles. but because the earth curves, the shortest distance is 3,605 miles and you go n.e. then e. and then s.e.

validation! by no less than hawking himself! yay!!!